Check out this jaw-dropping video of a natural phenomenon known as a "murmuration." The collective noun is used to describe vast numbers of starlings as they whirl through the air like billowing clouds of black, biological smoke.

This footage comes to you courtesy of Sophie Windsor Clive, who recently encountered the birds by chance while while canoeing the River Shannon in Ireland. According to The Telegraph's Daniel Butler, the appearance of murmurations tends to ramp up with the arrival of winter, and is actually a survival tactic; with predators in the area, it pays to seek safety in numbers.

Butler describes the mathematics behind the phenomenon:

Impenetrable as the flock's movements might seem to the human eye, the underlying maths is comparatively straightforward. Each bird strives to fly as close to its neighbours as possible, instantly copying any changes in speed or direction. As a result, tiny deviations by one bird are magnified and distorted by those surrounding it, creating rippling, swirling patterns. In other words, this is a classic case of mathematical chaos (larger shapes composed of infinitely varied smaller patterns).